Syllogistic with complex terms.
Arthur Baker · Notre Dame Journal of Formal Logic · 1972
Simple Terms In studies of classical syllogistic logic it has been shown how the theses of that logic can be axiomatized in accordance with the principles of modern logic.Thus J. Lukasiewicz 1 and I. M. Bocheήski 2 have axiomatized the ordinary system of positive terms-i.e., the system containing the 24 syllogistic moods and the 18 rules for conversion and opposition-by introducing four axioms and deducing the remaining theses as theorems.If we adopt Lukasiewicz's symbolism for expressing the A, E, /, O propositions of syllogistic (so that Aab is to be read "All a are b", etc.) and if, for clarity, we use Russellian-type symbolism for the propositional calculus, we can, for example, express Bocheήski's axioms as follows.System CS 51 Aaa 52 laa 53 Acb hAac^Aab (Barbara) 54 Ecb & lac D Oab (Ferio)When the theses for negative terms are added-i.e., when the rules for obversion and consequent rules for contraposition, etc. are introduced-the complete system of simple terms can be axiomatized.Thomas, in demonstrating this 3 , used the following axioms.System CS(n) 51 Aaa 52 laa